Solve (2010+1/2012):(1-1/2012)

$$( 2010 + \frac { 1 } { 2012 } ) : ( 1 - \frac { 1 } { 2012 } )$$

Evaluate

$$2011$$

Solution Steps

Convert 2010 to fraction \frac{4044120}{2012}.

$$\frac{\frac{4044120}{2012}+\frac{1}{2012}}{1-\frac{1}{2012}}$$

Since \frac{4044120}{2012} and \frac{1}{2012} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4044120+1}{2012}}{1-\frac{1}{2012}}$$

Add 4044120 and 1 to get 4044121.

$$\frac{\frac{4044121}{2012}}{1-\frac{1}{2012}}$$

Convert 1 to fraction \frac{2012}{2012}.

$$\frac{\frac{4044121}{2012}}{\frac{2012}{2012}-\frac{1}{2012}}$$

Since \frac{2012}{2012} and \frac{1}{2012} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4044121}{2012}}{\frac{2012-1}{2012}}$$

Subtract 1 from 2012 to get 2011.

$$\frac{\frac{4044121}{2012}}{\frac{2011}{2012}}$$

Divide \frac{4044121}{2012} by \frac{2011}{2012} by multiplying \frac{4044121}{2012} by the reciprocal of \frac{2011}{2012}.

$$\frac{4044121}{2012}\times \frac{2012}{2011}$$

Multiply \frac{4044121}{2012} times \frac{2012}{2011} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4044121\times 2012}{2012\times 2011}$$

Cancel out 2012 in both numerator and denominator.

$$\frac{4044121}{2011}$$

Divide 4044121 by 2011 to get 2011.

$$2011$$

Factor

$$2011$$